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A network model of a primitive cubic system The primitive and cubic close-packed (also known as face-centered cubic) unit cells. In crystallography, the cubic (or isometric) crystal system is a crystal system where the unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in crystals and minerals.
All primitive unit cells with different shapes for a given crystal have the same volume by definition; For a given crystal, if n is the density of lattice points in a lattice ensuring the minimum amount of basis constituents and v is the volume of a chosen primitive cell, then nv = 1 resulting in v = 1/n, so every primitive cell has the same ...
For face-centered cubic (fcc) and body-centered cubic (bcc) lattices, the primitive lattice vectors are not orthogonal. However, in these cases the Miller indices are conventionally defined relative to the lattice vectors of the cubic supercell and hence are again simply the Cartesian directions.
Now take one of the vertices of the primitive unit cell as the origin. Give the basis vectors of the real lattice. Then from the known formulae, you can calculate the basis vectors of the reciprocal lattice. These reciprocal lattice vectors of the FCC represent the basis vectors of a BCC real lattice.
The Wigner–Seitz cell, named after Eugene Wigner and Frederick Seitz, is a primitive cell which has been constructed by applying Voronoi decomposition to a crystal lattice. It is used in the study of crystalline materials in crystallography. Wigner–Seitz primitive cell for different angle parallelogram lattices.
In mathematics and solid state physics, the first Brillouin zone (named after Léon Brillouin) is a uniquely defined primitive cell in reciprocal space. In the same way the Bravais lattice is divided up into Wigner–Seitz cells in the real lattice, the reciprocal lattice is broken up into Brillouin zones. The boundaries of this cell are given ...
A three-dimensional crystal has three primitive lattice vectors a 1, a 2, a 3. If the crystal is shifted by any of these three vectors, or a combination of them of the form n 1 a 1 + n 2 a 2 + n 3 a 3 , {\displaystyle n_{1}\mathbf {a} _{1}+n_{2}\mathbf {a} _{2}+n_{3}\mathbf {a} _{3},} where n i are three integers, then the atoms end up in the ...
[2] For example, the matrix = transforms a primitive cell to body-centered. Another particular case of the transformation is a diagonal matrix (i.e., P i ≠ j = 0 {\textstyle P_{i\neq j}=0} ). This called diagonal supercell expansion and can be represented as repeating of the initial cell over crystallographic axes of the initial cell.